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    Beta coefficients in multiple regression




    Hi guys.

    I have a question about beta coefficients that are calculated
    for standard multiple linear regression procedure. I kind of don't understand
    about how they indeed are calculated. They are regression coefficients
    that occur when predictors are standardized to have zero mean and 1
    standard error. I thought they are just raw coefficients multiplied by
    corresponding raw predictor's standard errors. But it seems like it's not true.

    Any thoughts on how they are calculated ?

    Thanks in advance.

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    It is exactly what you said. you standardize the predictors first (from each variable or column you subtract its mean and divide by the standard deviation) and then you perform the classical multiple linear regression. But their interpretation is also a bit different.

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    Quote Originally Posted by kobylkinks View Post

    Any thoughts on how they are calculated ?

    Thanks in advance.

    You can compute the j-th standardized regression weight as:

    beta_j = b_j * (S_j / S_Y) where

    b_j is the usual OLS unstandardized regression weight and S_j and S_Y are the standard deviations associated with the j-th independent variable and the dependent variable (Y), respectively.


    Note: If you want to compute them through a regression analysis you have to standardize all variables including the dependent variable (Y) before perfoming the regression.

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    Quote Originally Posted by Dragan View Post
    You can compute the j-th standardized regression weight as:

    beta_j = b_j * (S_j / S_Y) where

    b_j is the usual OLS unstandardized regression weight and S_j and S_Y are the standard deviations associated with the j-th independent variable and the dependent variable (Y), respectively.


    Note: If you want to compute them through a regression analysis you have to standardize all variables including the dependent variable (Y) before perfoming the regression.

    Thank you. I'm using StatSoft Statistica. It computes both B and Beta coefficients. So beta coefficients look like correlations, right ? At least it's true for one-variable regression analysis.

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    I know this is an old thread, but I thought I'd mention that STATISTICA has different representations of regression coefficients.

    Prior to Version 9:
    • Beta: standardized
    • B: non-standardized

    Version 9 and beyond:
    • b*: standardized
    • b: non-standardized

    The standardized beta (b*) are the coefficients you would have obtained had you first standardized all of your variables to a mean of 0 and a standard deviation of 1. Thus, the magnitude of these b* coefficients allow you to compare the relative contribution of each independent variable in the prediction of the dependent variable.

    The non-standardized beta (b) is used more generally.

    From the Multiple Regression Results dialog, you can access values for both the standardized beta (b*) and the non-standardized beta (b) by clicking the "Regression results" button.

    Hope this helps...
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    Last edited by JenB; 10-06-2009 at 10:59 AM. Reason: added picture

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